Optimisation approach for parameter estimation of the generalised PTT viscoelastic model

The exponential form of the original Phan-Thien and Tanner (PTT) model is often used to study complex viscoelastic fluids. Recently, a generalised version of the PTT model, that uses the Mittag-Leffler function to compute a new function of the trace of the stress tensor, was proposed. This new model adds one or two additional fitting parameters that allow for greater fitting capability. In this paper, we propose two optimisation problems for estimating the model parameters when fitting experimental data in shear (storage modulus, loss modulus, shear viscosity). We also propose a numerical sequential approach for solving one of these problems. The optimal values for the parameters produced by the optimisation approach allow the model to reproduce almost exactly the experimental data.
Supported by FCT -Fundacao para a Ciencia e a Tecnologia, through projects UIDB/00013/2020 and UIDP/00013/2020, and CMAT -Centre of Mathematics, University of Minho.